Inner-city constituencies are among the worst in the country for access to super-fast broadband, according to new figures from the Department for Culture, Media and Sport.

Despite the department’s £1.7bn investment in extending Britain’s internet infrastructure to under-served areas, constituencies in London and Hull will languish at the bottom of the league table once the improvements bear fruit in 2017. The government says it is unable to directly invest in those areas because competition rules prevent state intervention.

The Cities of London and Westminster, which is the constituency of Conservative MP Mark Fields, will fare worst, with only 31% of premises having access to super-fast connections, defined as those with speeds above 24 megabits a second, as of August 2014.

The bottom 20 constituencies will all have super-fast penetration of less than 76% once the works are complete. Of those, 12 are rural constituencies that have received government funding to increase broadband reach, in some cases bringing them from zero connected homes and businesses to 75% penetration in one go.

Of the remaining eight constituencies with poor access to high-speed internet, three are in Kingston-upon-Hull, where the city’s unique history of locally-operated telecommunications firms has left central government with little ability to affect infrastructure.

The final five, including the worst constituency in the country, are in the capital. As well as the Cities of London and Westminster, the constituencies are Bermondsey and Old Southwark, Bethnal Green and Bow, Poplar and Limehouse and Westminster North. All five form a contiguous area in central London, and contain some of the most deprived areas of inner London.

But because the constituencies are in inner-city locations ostensibly well-served by commercial provision, the government says it is not allowed to directly invest in improving infrastructure in the same way it does in rural areas.

The telecoms companies, by contrast, point out that certain areas of central London have few residential households, making it uneconomical to invest in access for those few that remain.

A DCMS spokesperson said: “State aid rules ensure government only builds network where the commercial sector won’t go and BT, Virgin and others have already announced plans for commercial roll out in cities – including a £50m investment from BT. We are already reviewing what we can do for residents in those areas the market won’t reach as part of our commitment to take super-fast broadband to the final 5%.

“In order to drive the economy we have already seen over 8,000 businesses in UK cities benefit from faster and better broadband as part of our successful connection voucher scheme.”

The Guardian understands that 85% of the costs of expanding the broadband network in the capital are so-called “civil” costs, such as planning regulations and other red tape. For instance, while electricity and gas companies can connect properties on a compulsory-purchase basis, and pay compensation to the property owner, landlords can name their price to ISPs – a crucial factor in parts of the city where new-builds and rented accommodations dominate.

London has near-universal access to broadband at speeds less than 24Mbps, and BT says that additionally every business in the city has access to super-fast broadband. But it still leaves the odd situation where parts of London are, on paper, less well-connected than some of the most rural areas of Britain.

Rushanara Ali, Labour MP for Bethnal Green and Bow, described the failure is “ludicrous”.

“The government has failed to deliver super-fast broadband to the UK on time and on budget. Urban areas are being left behind. For my inner-London constituency of Bethnal Green and Bow, bordering Tech City, this is nothing short of ludicrous.

“Not only is the government letting down thousands of households in the East End, it’s also threatening the growth of local businesses, which depend on hi-tech infrastructure to flourish.”

Jim Fitzpatrick, Labour MP for Poplar and Limehouse, adds that he regularly raises the issue with ISPs. “It’s dreadful for some,” he told the Guardian, “especially those close to Canary Wharf, which has superfast links”.

Virgin Media said that it was working to bring super-fast broadband to more urban areas. “We announced last year an expansion to 100,000 new homes in a number of London boroughs in the east, ranging from Shoreditch/Brick Lane eastwards as far as Barking. This was the single largest expansion since Virgin Media launched in 2007,” a Virgin spokesman told the Guardian.